Question: The number of cans in the layers of a display in a supermarket form an arithmetic sequence. The bottom layer has 28 cans; the next layer has 25 cans and so on until there is one can at the top of the display. How many cans are in the entire display?
The arithmetic series is $1 + 4 + \cdots + 25 + 28$, with a common difference of 3. Suppose there are $n$ terms in the series. Then 28 is the $n$th term, so $1 + (n-1)\cdot 3 = 28$. Solving, we get $n = 10$. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum is $(1 + 28)/2 \cdot 10 = \boxed{145}$.